Find a wall stud. Either buy an electrical stud finder and run it along your wall or manually measure for a stud. Studs are typically located at 16-inch increments, anchored at a wall outlet. Knock on the wall to test for a stud -- if the sound is hollow, you have not located a stud. You can also drill into a test spot, and if the drill experiences resistance you have reached a stud. Baseboards are nailed into studs, so if you can find a nail in your baseboard, you can use that as a guide.
Determine where on the grandfather clock you want to attach a bracket. Using a tape measure, figure out how many inches from the ground the bracket will be. Apply the same measurement to the wall, and make a mark with a pencil. For instance, if the place on the clock where the bracket will be attached is 60 inches from the ground, make a pencil mark on the wall 60 inches from the floor.
Drill a hole into the wall on the pencil mark. Make the hole slightly smaller than the screw you intend on using to attach the wall bracket.
Screw the wall bracket into the wall and the other bracket into the back of your clock.
Position the grandfather clock in front of the wall bracket and attach the two brackets using the strap provided. In some cases, the strap may be attached to the wall bracket, while in others the strap is a third piece that needs to be looped through both pieces. Once the strap is in place, you can move the furniture closer to the wall if you want to.